Differential games through viability theory : old and recent results.

This article is devoted to a survey of results for differential games obtained through Viability Theory. We recall the basic theory for differential games (obtained in the 1990s), but we also give an overview of recent advances in the following areas : games with hard constraints, stochastic differential games, and hybrid differential games. We also discuss several applications.Game theory; Differential game; viability algorithm;

A suggestion for simplifying the theory of asset prices

Using an ordinal approach to utility, in the spirit of Hicks (1962, 1967a), it is possible to greatly simplify the theory of asset prices. The basic assumption is to summarize any probability distribution into its moments so that preferences over distributions can be mapped into preferences over vectors of moments. This implies that assets, like Lancaster’s (1966) consumption goods, are bundles of characteristics and can be directly priced, at the margin, in terms of the market portfolio. Expected utility is not required and both St.Petersburg and Allais paradoxes may be easily solved

A suggestion for simplifying the theory of asset prices

Using an ordinal approach to utility, in the spirit of Hicks (1962, 1967a), it is possible to greatly simplify the theory of asset prices. The basic assumption is to summarize any probability distribution into its moments so that preferences over distributions can be mapped into preferences over vectors of moments. This implies that assets, like Lancaster’s (1966) consumption goods, are bundles of characteristics and can be directly priced, at the margin, in terms of the market portfolio. Expected utility is not required and both St.Petersburg and Allais paradoxes may be easily solved

Growth Optimal Investment and Pricing of Derivatives

We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant to the problem of pricing derivatives. We compare our result with other alternative pricing procedures in the literature, and discuss the limits of validity of the lognormal approximation. We also generalize the pricing method to a market with correlated stocks. The expected estimation error of the optimal investment fraction is derived in a closed form, and its validity is checked with a small-scale empirical test.Comment: 21 pages, 5 figure